limits question! please help

Question

anonymous · Answer

attachment

debbieg · Answer

Is part of the problem missing?? What about $$\Large \lim_{x \rightarrow a}f(x)~~??$$

I'm going to assume that it is supposed to say determine values where $$\Large \lim_{x \rightarrow a}f(x)=f(a)$$


you only have to worry about the places in the domain where you "crossover" from one rule to another, or x=0. In other words, everywhere else in the domain, it's clearly true. (do you see why?)

so you just need to examine what happens at each of those points: x=-2, x=0, and x=2.

For it to be true that $$\Large \lim_{x \rightarrow a}f(x)=f(a)$$ it has to be true that f(a) exists, and that the limits from the left and from the right are both equal to f(a).

anonymous · Answer

@DebbieG so If I were to write that in interval notation, would it be 
(−∞, −2)∪(−2, 0)∪(0,2)∪(2,∞) ?

debbieg · Answer

Did you check all of those x's? Did you determine if it's true or false at x=-2, x=0 and x=2?

debbieg · Answer

(That is, assuming that the question is what I stated above, because part of the question seems to be missing from the image??)

anonymous · Answer

@DebbieG  actually no, it's not missing. I don't understand to be quite honest.

debbieg · Answer

Well, if you can email your instructor you might ask. there is definitely something missing.

I'm assuming that the question is:

Determine all values of a where $$\Large \lim_{x \rightarrow a}f(x)=f(a)$$
but frankly.... it could just as well be "all values of a where $$\Large \lim_{x \rightarrow a}f(x)\neq f(a)$$ lol.... so really, kind of a toss up. But obviously, the solution to one is just the reverse of the solution to the other.... either way, you have to find where it IS or ISNT true.

So if you check at x=-2, x=0 (that one is trivial - since f(0) is undefined, clearly not true there... right?) and x=2, whether:

$$\Large \lim_{x \rightarrow a}f(x)=f(a)$$

I am pretty sure that it IS true at one of $\pm2$, and NOT true at the other.  But you have to check! :)

debbieg · Answer

Just plug x=-2 into each of the first 2 "chunks" of the function definition (the one that really IS the function for x=-2, and the one that is for x<-2). See if they are equal.

Then do the same for x=2.